In order to have a visual impression of the correlation between the location of the TDs and the PEs we present in Fig. REF (e) the charge density field of these TDs (color map) as well as the location of the PEs (symbols). The graph demonstrates the strong correlation between zones with a high density of \(-1\)  TDs and the PEs. (This strong correlation becomes even more visible if we just consider the \(-1\)  TDs to generate the colormap, see Extended Data Fig. REF .) One also notices that basically all zones of high density do contain PEs, i.e., the negative TDs are indeed able to predict the location of the “soft spots”, the points at which the sample is yielding. Note that we have done the shearing in the \(+x\)  and the \(-x\)  direction and, as expected, the location of the corresponding plastic events (filled and open symbols) are not quite the same. However, both types of PEs do show a good correlation with the zones of strong negative charge, i.e., to a first approximation the tensorial character of the plastic response can be neglected. One also recognizes clearly the anti-correlation between the PE and the positive TDs (zones in red), showing that the former are forming “hard spots” in the samples that are stable under a shear transformation. This result is reasonable since the positive TDs correspond to the points of the vibrational excitations at which the vibrational amplitude goes smoothly to zero and hence it can be expected that the nearby particles will not be affected strongly by the external shear. This rational is consistent with earlier findings that particles with larger amplitude of the vibrational eigen-vector contribute more to the non-affine deformation and thus irreversible rearrangements [1]}, [2]}.
